Does theta(n^3+2n+1) = theta(n^3) hold? Justify your answer.
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Determine if (n!) converges, and justify your answer. (2n)! n=1
Determine whether the following series converge or diverge. Fully justify your answer. T(-1)"(n? – 2n) 400n3 + 78972 2
tan-i (-1+-- 2. Express the limit lini Σ 2n 2 as a definite n 2n integral. Make sure to fully justify your work. Hint: What is equal to? tan-i (-1+-- 2. Express the limit lini Σ 2n 2 as a definite n 2n integral. Make sure to fully justify your work. Hint: What is equal to?
1. Answer the following questions. Justify your answers. (a) (3 marks) For what values of x does the series 1 + 22x 2 + 24x 4 + 26x 6 · · · + 22nx 2n + · · · converge? (b) (9 marks) Is the following series absolutely convergent, conditionally convergent or divergent? i. X∞ n=1 2 √ n − 2 √ n + 1 ii. X∞ n=1 arctan(n) n2 + 1 iii. X∞ k=1 (−1)k k 1. Answer the...
Among the following series, which one does converge conditionally? n=1 Σ(-1)"re-n 1-3-5 3 3-5 3-5.7 1-3-5(2n-1 -(2n) 1.3.5 (2n-1) (-1)" n=1 Σ(-1)"re-n 1-3-5 3 3-5 3-5.7 1-3-5(2n-1 -(2n) 1.3.5 (2n-1) (-1)"
,,tan-ı(-1 + n-2n). 2. Express the limithu 2 as a definite k-1 integral. Make sure to fully justify your work. Hint What is equal to? ,,tan-ı(-1 + n-2n). 2. Express the limithu 2 as a definite k-1 integral. Make sure to fully justify your work. Hint What is equal to?
Test the series for convergence or divergence clearly justify sin(2n) 1+21 n=1
1 2 3 n-9n2 1. Consider an = 1+ 2n - 5n2 (a) (3 points) Does the sequence {an} converge or diverge? Show your work. (b) (3 points) Does the series an converge or diverge? Why? 2. (8 points) Use a comparison test to state whether the given series converges or diverges. 3. (6 points) Does the given series converge or diverge? If it converges, what is its sum? § (cos(n) – cos(n + 1))
4. Select a theta notation chosen from Olign) , O(n), O(nlgn), o(na), O(nk) If your answer is o link), specify the Constant k. a) 2n?+!. b) 3 n²+ anlgn c). 6n6 +n+4 d) 2+4 +6+un+an e) (6n +4) (1 + Ign) - Type here to search o A e - a
Determine if the series 2n=1(-1)"(1 – 2n)" converges (C) or diverges (D). Justify your conclusion for C or D by showing all your work and indicating all test names that you used and conditions for conclusions. NO justification, NO credit! (Test names : Geo, NT, IT(P — series test), DCT, LCT, ACT, AST, RT, NRT)